Two straight lines cut the -axis at and respectively and cut the -axis at and…
MATHEMATICS · Multi-part · AoPS · Mathematics · Multi-Variable Linear Equations · Multi-Variable Linear Equations
Problem
Two straight lines cut the x-axis at (a,0) and (c,0) respectively and cut the y-axis at (0,b) and (0,d) respectively.
(i) Explain how the values of a,b,c, and d can be used to write each line first in intercept form and then in standard form Ax+By+C=0.
(ii) Describe, without performing any calculation, how you would decide from a sketch of the two lines whether the pair of equations will have (a) one solution, (b) no solution, or (c) infinitely many solutions.
(iii) Give one numerical example for each of the three cases mentioned in part (ii) and justify your answer briefly.